So carry on!
Again, what do you notice? Have a chat to someone else about it.

D. We could use two rules, but only changing one at a time - I'll show you what I mean. Suppose we use "add ... then multiply by 9" and have "adding 1" as a first idea.
Starting with
1 we'd have : 1 8 1 8 1 8 1 8 1 8 1 8
2 we'd have : 2 7 2 7 2 7 2 7 2 7 2 7
3 we'd have : 3 6 3 6 3 6 3 6 3 6 3 6

... so carry on.

But we could add 2 or 3 or 4 ... each time instead and explore the nine patterns each time.
So, for example, adding on 5 then multiplying by 9 we get the following 9 patterns

1 4 1 4 1 4 1 4 1 4 1 4

2 3 2 3 2 3 2 3 2 3 2 3

3 2 3 2 3 2 3 2 3 2 3 2

4 1 4 1 4 1 4 1 4 1 4 1

5 0 5 0 5 0 5 0 5 0 5 0

6 9 6 9 6 9 6 9 6 9 6 9

7 8 7 8 7 8 7 8 7 8 7 8

8 7 8 7 8 7 8 7 8 7 8 7

9 6 9 6 9 6 9 6 9 6 9 6

E. You may be getting the idea. You could use any combination of rules.

What about using division?

Those of you with spreadsheet skills could use these ideas to explore quite far!

It is through investigations like this that you have opportunities of exploring and extending knowledge of many different aspects of number work. In this activity there are opportunities to work on repeat patterns, reflective patterns, number patterns related to tables, addition, subtraction, multiplication, setting further challenges, systematic working and perseverance.

Many of the patterns that are generated almost duplicate others. For example if the rule is to multiply by 3, this is what you get starting with each digit in turn: